cp's OEIS Frontend

A266568 a(n) = smallest k such that 2^k ends in a string of exactly n nonzero digits.

%I A266568 #7 Jan 01 2016 20:16:55
%S A266568 0,4,7,13,14,18,50,24,27,31,34,37,68,93,49,51,116,214,131,155,67,72,
%T A266568 76,77,81,86,149,498,154,286,359,866,1225,329,664,129,573,176,655,820,
%U A266568 571,434,1380,475,1260,2251,6015,3066,1738,2136,2297,432,665,229,1899
%N A266568 a(n) = smallest k such that 2^k ends in a string of exactly n nonzero digits.
%C A266568 Since 2^a(n) must have at least n digits, a(n) >= (n-1)*log_2(10).
%C A266568 The 26-digit number 2^86 = 77371252455336267181195264 is almost certainly the largest power of 2 that contains no zero digit.
%C A266568 A notably low local minimum occurs at a(36) = 129, which is less than a(n) for all n > 26.
%C A266568 A notably high local maximum occurs at a(122) = 11267047.
%e A266568 2^0 = 1 is the smallest power of 2 ending in a string ("1") of exactly 1 nonzero digit, so a(1) = 0.
%e A266568 2^4 = 16 is the smallest power of 2 ending in a string ("16") of exactly 2 nonzero digits, so a(2) = 4.
%e A266568 2^50 = 1125899906842624 is the smallest power of 2 ending in a string ("6842624") of exactly 7 nonzero digits, so a(7) = 50.
%e A266568 The last 7 digits of 2^24 = 16777216 -- i.e., "6777216" -- are also nonzero, but so is the preceding digit, so 2^24 ends in a string of exactly 8 nonzero digits. Since no smaller power of 2 ends in exactly 8 nonzero digits, a(8) = 24.
%Y A266568 Cf. A007377, A031140, A031141, A031142, A031143, A181611.
%K A266568 nonn,base
%O A266568 1,2
%A A266568 _Jon E. Schoenfield_, Jan 01 2016